Here is the full list of all 23 Destiny or Fate achievements.
Slay 50 elites.
Slay 1000 normal monsters.
Gain 10,000 golds.
Gain 1,000,000 golds.
Slay boss, Draga.
Slay boss, Hydra.
Slay boss, Scythe.
Slay boss, Skeleton King.
Finish the story with one hero.
Finish the story with five heroes.
Finish the story with ten heroes.
Finish the story with all heroes.
10 Defeats.
Defeat for the first time.
Slay boss, Yacha.
Complete Chapter.3
Complete Chapter.2
Slay boss, Zatorich.
Complete Chapter.1
Slay first elite.
Arrive in shop block for the first time.
Get mastery for the first time.
Improve your hero via Enchant Point